reserve GS for GraphStruct;
reserve G,G1,G2,G3 for _Graph;
reserve e,x,x1,x2,y,y1,y2,E,V,X,Y for set;
reserve n,n1,n2 for Nat;
reserve v,v1,v2 for Vertex of G;

theorem Th53:
  for G1 being _Graph, E being set, G2 being removeEdges of G1,E
holds the_Vertices_of G2 = the_Vertices_of G1 & the_Edges_of G2 = the_Edges_of
  G1 \ E
proof
  let G1 be _Graph, E be set, G2 be removeEdges of G1,E;
  set V = the_Vertices_of G1;
  V c= V;
  then reconsider V as non empty Subset of the_Vertices_of G1;
  set E2 = the_Edges_of G1 \ E;
  reconsider E2 as Subset of G1.edgesBetween(V) by Th34;
  G2 is inducedSubgraph of G1,V,E2;
  hence thesis by Def37;
end;
